Stephen Dawe, 36, is accused of ripping a handrail out of the wall as he ascended the iconic London landmark along with Archit Ssan, 55.
The men belong to the activist group New Fathers 4 Justice, a fathers' rights protest group campaigning for the rights of fathers to see their children.
At Westminster magistrates' court, Ssan and Dawe denied the charges of obstructing a person engaged in a lawful activity and aggravated trespass.
Dawe also denies an additional charge of criminal damage.
In a blog post on the New Fathers 4 Justice website dated 6th October 2016, Ssan said he chose to scale St Paul's to draw attention to what he perceives as bias in the family court system.
Ssan wrote: "In child custody cases, more often than not, near total custody is retained by the mother. The best deal that fathers can hope for is seeing their child on every other weekend and that's if everything goes smoothly.
"Understandably this has a disastrous impact on both parties, with children largely losing touch with their loving fathers and fathers experiencing intense emotional distress at not being able to see their children regularly."